Problem: Expand the product ${(2x+3)(x+5)}$.
Solution: When using the distributive property for the first time, we add the product of $2x+3$ and $x$ to the product of $2x+3$ and 5:

\begin{align*}
(2x+3)(x+5) &= (2x+3) \cdot x + (2x+3) \cdot 5\\
&= x(2x+3) + 5(2x+3)
\end{align*}We use the distributive property again and combine like terms:

\begin{align*}
x(2x+3) + 5(2x+3) &= 2x^2 + 3x + 10x+ 15\\
&= \boxed{2x^2 + 13x + 15}
\end{align*}